Mathematical modeling—the ability to apply mathematical concepts and techniques to real-life systems—has expanded considerably over the last decades, making it impossible to cover all of its aspects in one course or textbook. Continuum Modeling in the Physical Sciences provides an extensive exposition of the general principles and methods of this growing field with a focus on applications in the natural sciences. The authors present a thorough treatment of mathematical modeling from the elementary level to more advanced concepts.

Most of the chapters are devoted to a discussion of central issues such as dimensional analysis, conservation principles, balance laws, constitutive relations, stability, robustness, and variational methods, and are accompanied by numerous real-life examples. Readers will benefit from the exercises placed throughout the text and the Challenging Problems sections found at the ends of several chapters. The last chapter is devoted to extensively worked-out case studies in polymer dynamics, fiber spinning, water waves, and waveguide optics.

AudienceThis book is intended for advanced undergraduate and graduate students in mathematics. It would also be a useful reference for physicists, chemists, biologists, and natural scientists, as well as engineers in the mechanical, electrical, chemical, geophysical, and manufacturing fields.

About the AuthorsE. van Groesen is a Professor in the Department of Applied Mathematics at the University of Twente, The Netherlands. He is also Chair of the Applied Analysis and Mathematical Physics Group, which is part of the Department of Applied Mathematics. His research interests are mathematical optics and fluid dynamics.

Jaap Molenaar is a Professor and Head of the Applied Mathematics Group, Biometris, at Wageningen University and Research Centre, The Netherlands. He is editor-in-chief of the quarterly magazine of the Royal Dutch Mathematics Society. For more than a decade he was involved in consulting work for industry and received the Neways Award for his promotion of the transfer of academic knowledge to industry. His research focuses on fluid mechanics, in particular polymer melt flow and systems biology.